A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly…
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability, that a student will get 4 or more correct answers just by guessing, is
$\frac{10}{3^5}$
$\frac{17}{3^5}$
$\frac{13}{3^5}$
$\frac{11}{3^5}$
Solution
Probability of guessing correct answer be
$p=\frac{1}{3}$
$\therefore \quad \mathrm{q}=\frac{2}{3}$
Let random variable X denotes the number of correct answers.
$\begin{array}{ll}
\therefore \quad & X \sim B\left(5, \frac{1}{3}\right) \\
\therefore \quad & \text { Required probability }=\mathrm{P}(\mathrm{X} \geq 4) \\
& =\mathrm{P}(\mathrm{X}=4)+\mathrm{P}(\mathrm{X}=5) \\
& ={ }^5 \mathrm{C}_4\left(\frac{1}{3}\right)^4\left(\frac{2}{3}\right)+{ }^5 \mathrm{C}_5\left(\frac{1}{3}\right)^5 \\
& =5 \times \frac{2}{3^5}+\frac{1}{3^5} \\
& =\frac{11}{3^5}
\end{array}$